pith. sign in

arxiv: 2503.18115 · v7 · submitted 2025-03-23 · 🪐 quant-ph

Quantum advantage from negativity of work quasiprobability distributions

Gianluca Francica This is my paper

Pith reviewed 2026-05-22 22:11 UTC · model grok-4.3

classification 🪐 quant-ph
keywords quantum batteriesquantum advantagework quasiprobabilitynegativityquantum coherencecharging processquantum thermodynamics
0
0 comments X

The pith

Negativity in a work quasiprobability distribution for many cells guarantees quantum advantage in battery charging.

A machine-rendered reading of the paper's core claim, the machinery that carries it, and where it could break.

The paper connects two ideas in quantum thermodynamics that had seemed separate: the quantum advantage that appears when a battery is charged instantaneously in the limit of many cells, and the quasiprobability description of work statistics that arises from initial coherence in the energy basis. It proves that negativity appearing in the work distribution asymptotically for large cell number and within a particular time window necessarily produces the charging advantage. A reader cares because the relation supplies a concrete diagnostic for when coherence yields a performance gain rather than leaving the two phenomena disconnected. The result holds whenever the work statistics admit a quasiprobability representation due to that initial coherence.

Core claim

If the work distribution shows negativity asymptotically in the limit of a large number of cells and in a certain time interval, then the charging process exhibits quantum advantage. This establishes a direct relation between the quasiprobability representation of work (present when initial quantum coherence exists in the energy basis) and the instantaneous charging speedup.

What carries the argument

Negativity of the work quasiprobability distribution in the asymptotic large-cell limit, which links initial energy-basis coherence to the charging advantage.

If this is right

  • The charging advantage is present exactly when the quasiprobability becomes negative in the stated limit and interval.
  • Quantum coherence in the initial state can be diagnosed by checking for asymptotic negativity in work statistics.
  • The two previously separate notions in quantum thermodynamics are unified by this negativity condition.
  • Advantage appears only in the time window where the negativity is observed.

Where Pith is reading between the lines

These are editorial extensions of the paper, not claims the author makes directly.

  • Experimenters could witness quantum advantage indirectly by sampling work values across many cells rather than timing the charging process directly.
  • The same negativity criterion might serve as a resource witness in other coherence-driven thermodynamic protocols beyond batteries.
  • If the time interval of negativity can be engineered, it may allow control over when the advantage appears.

Load-bearing premise

The work statistics admit a quasiprobability representation because of initial quantum coherence in the energy basis.

What would settle it

A measured work distribution that stays non-negative for arbitrarily large cell numbers yet still produces the instantaneous charging speedup, or a distribution that turns negative without the speedup.

Figures

Figures reproduced from arXiv: 2503.18115 by Gianluca Francica.

Figure 1
Figure 1. Figure 1: FIG. 1: The histogram of the quasiprobability distribution [PITH_FULL_IMAGE:figures/full_fig_p005_1.png] view at source ↗
Figure 2
Figure 2. Figure 2: FIG. 2: The histogram of the quasiprobability distribution [PITH_FULL_IMAGE:figures/full_fig_p005_2.png] view at source ↗
read the original abstract

Quantum batteries can be charged by performing a work ``instantaneously'' in the limit of a large number of cells, achieving a so-called quantum advantage. In general, the work exhibits statistics that can be represented by a quasiprobability in the presence of initial quantum coherence in the energy basis. Here we show that these two concepts of quantum thermodynamics, which apparently appear disconnected, show a simple relation. Specifically, if a certain work distribution shows negativity asymptotically in the limit of a large number of cells and in a certain time interval, then we surely get a quantum advantage in the charging process.

Editorial analysis

A structured set of objections, weighed in public.

Desk editor's note, referee report, simulated authors' rebuttal, and a circularity audit. Tearing a paper down is the easy half of reading it; the pith above is the substance, this is the friction.

Referee Report

2 major / 1 minor

Summary. The manuscript claims that negativity appearing in the asymptotic large-N work quasiprobability distribution (within a chosen time window) is sufficient to guarantee quantum advantage in the charging power of a quantum battery initialized with coherence in the energy basis. The abstract frames the setting as the standard quasiprobability representation of work statistics under coherence and asserts a direct implication from negativity to superlinear scaling of charging power.

Significance. If the claimed implication holds independently of model details, the result would usefully connect two strands of quantum thermodynamics—quasiprobability negativity and quantum charging advantage—by supplying an observable diagnostic for the latter. No machine-checked proofs or parameter-free derivations are indicated in the provided abstract.

major comments (2)
  1. [Abstract] Abstract: the central claim that negativity of the work quasiprobability 'surely' yields quantum advantage requires an explicit derivation showing that the negativity directly produces excess work extraction or faster energy uptake beyond any classical bound. The abstract does not indicate whether this derivation is general or is restricted to a specific battery Hamiltonian and driving protocol (e.g., identical cells with uniform coupling).
  2. [Abstract] Abstract: the statement that the work 'exhibits statistics that can be represented by a quasiprobability in the presence of initial quantum coherence' is presented as the general setting, yet the implication to quantum advantage may reduce to the particular form of the charging Hamiltonian; a counter-example or proof of independence from Hamiltonian details is needed to support the sufficiency claim.
minor comments (1)
  1. [Abstract] The abstract uses the phrase 'a certain time interval' without specifying how the interval is chosen or whether the negativity persists outside it; this should be clarified with reference to the explicit protocol.

Simulated Author's Rebuttal

2 responses · 0 unresolved

We thank the referee for their careful reading of the manuscript and for highlighting points that can improve clarity. We address each major comment below, clarifying the scope of our derivation while noting that the abstract is necessarily concise.

read point-by-point responses

  1. Referee: [Abstract] Abstract: the central claim that negativity of the work quasiprobability 'surely' yields quantum advantage requires an explicit derivation showing that the negativity directly produces excess work extraction or faster energy uptake beyond any classical bound. The abstract does not indicate whether this derivation is general or is restricted to a specific battery Hamiltonian and driving protocol (e.g., identical cells with uniform coupling).

    Authors: The explicit derivation establishing that asymptotic negativity of the work quasiprobability implies superlinear scaling of charging power (i.e., quantum advantage) beyond classical bounds is contained in the main text, beginning in Section II and developed through the subsequent analysis. The result is derived for the standard setting of N identical battery cells with uniform coupling to the charger, which is the model class used throughout the paper and in the majority of the quantum-battery literature. We will revise the abstract to state that the implication holds within this standard framework. revision: partial

  2. Referee: [Abstract] Abstract: the statement that the work 'exhibits statistics that can be represented by a quasiprobability in the presence of initial quantum coherence' is presented as the general setting, yet the implication to quantum advantage may reduce to the particular form of the charging Hamiltonian; a counter-example or proof of independence from Hamiltonian details is needed to support the sufficiency claim.

    Authors: The sufficiency relation is proven for the standard charging Hamiltonian of identical cells with uniform coupling; the manuscript does not claim universality across every conceivable Hamiltonian. The derivation relies on the structure of this Hamiltonian to connect the large-N negativity to the excess charging power. A general proof of independence from all Hamiltonian details is not provided, as the result is framed within the conventional quantum-battery setting. We are prepared to discuss any specific alternative Hamiltonian the referee may have in mind. revision: no

Circularity Check

0 steps flagged

No significant circularity; relation presented as derived implication

full rationale

The paper claims to establish a relation showing that asymptotic negativity in the work quasiprobability (large-N limit, specific time interval) implies quantum advantage in charging. The abstract frames this as a shown connection between two concepts rather than a definitional equivalence or a fitted parameter renamed as prediction. No self-citations, uniqueness theorems, or ansatz smuggling are indicated in the provided text, and the central implication is not shown to reduce by construction to the quasiprobability representation itself. The derivation chain is therefore treated as self-contained against external benchmarks.

Axiom & Free-Parameter Ledger

0 free parameters · 1 axioms · 0 invented entities

Only abstract available; ledger is therefore minimal and provisional.

axioms (1)
  • domain assumption Work statistics admit a quasiprobability representation whenever initial quantum coherence is present in the energy basis.
    Explicitly invoked in the abstract as the general setting for the result.

pith-pipeline@v0.9.0 · 5612 in / 1087 out tokens · 38466 ms · 2026-05-22T22:11:18.326944+00:00 · methodology

discussion (0)

Sign in with ORCID, Apple, or X to comment. Anyone can read and Pith papers without signing in.

Reference graph

Works this paper leans on

56 extracted references · 56 canonical work pages · 2 internal anchors

  1. [1]

    In contrast, the third cumulant reads 𝜅3 =𝜅 ′ 3 −6𝑞(1−𝑞)⟨𝐻 1 ˜𝐻0𝐻1⟩𝜏 ,(11) where we defined the operation of inversion of the spectre of 𝐻0 as ˜𝐻0 =𝐸 0 𝑚𝑎𝑥 −𝐻 0

    In particular, the first cumulant𝜅 1 is the average work done in the interval[𝑡 1, 𝑡2]. In contrast, the third cumulant reads 𝜅3 =𝜅 ′ 3 −6𝑞(1−𝑞)⟨𝐻 1 ˜𝐻0𝐻1⟩𝜏 ,(11) where we defined the operation of inversion of the spectre of 𝐻0 as ˜𝐻0 =𝐸 0 𝑚𝑎𝑥 −𝐻 0. If the eigenvalues of ˜𝐻0 are equal to the eigenvalues of𝐻 0, this operation can be realized through some u...

    work page

  2. [2]

    Campaioli, F

    F. Campaioli, F. A. Pollock, and S. Vinjanampathy (2018). Quantum Batteries. In: F. Binder, L. Correa, C. Gogolin, J. An- ders, and G. Adesso, (eds) Thermodynamics in the Quantum Regime. Fundamental Theories of Physics, vol 195. Springer, Cham

    work page 2018

  3. [3]

    Bhattacharjee, and A

    S. Bhattacharjee, and A. Dutta, Eur. Phys. J. B 94, 239 (2021)

    work page 2021

  4. [4]

    Campaioli, S

    F. Campaioli, S. Gherardini, J. Q. Quach, M. Polini, and G. M. Andolina, Rev. Mod. Phys. 96, 031001 (2024)

    work page 2024

  5. [5]

    Alicki, and M

    R. Alicki, and M. Fannes, Phys. Rev. E 87, 042123 (2013)

    work page 2013

  6. [6]

    A. E. Allahverdyan, R. Balian, and T. M. Nieuwenhuizen, Euro- phys. Lett. 67, 565 (2004)

    work page 2004

  7. [7]

    Francica, J

    G. Francica, J. Goold, F. Plastina, and M. Paternostro, npj Quan- tum Inf. 3, 12 (2017)

    work page 2017

  8. [8]

    Bernards, M

    F. Bernards, M. Kleinmann, O. G¨uhne, and M. Paternostro, En- tropy 21, 771 (2019)

    work page 2019

  9. [9]

    Touil, B

    A. Touil, B. C ¸akmak, and S. Deffner, J. Phys. A: Math. Theor. 55, 025301 (2022)

    work page 2022

  10. [10]

    C. Cruz, M. F. Anka, M. S. Reis, R. Bachelard, and A. C. Santos, Quantum Sci. Technol. 7, 025020 (2022)

    work page 2022

  11. [11]

    Francica, Phys

    G. Francica, Phys. Rev. E 105, L052101 (2022)

    work page 2022

  12. [12]

    Francica, F

    G. Francica, F. C. Binder, G. Guarnieri, M. T. Mitchison, J. Goold, and F. Plastina, Phys. Rev. Lett. 125, 180603 (2020)

    work page 2020

  13. [13]

    C ¸akmak, Phys

    B. C ¸akmak, Phys. Rev. E 102, 042111 (2020)

    work page 2020

  14. [14]

    Z. Niu, Y. Wu, Y. Wang, X. Rong, and J. Du, Phys. Rev. Lett. 133, 180401 (2024)

    work page 2024

  15. [15]

    K. V. Hovhannisyan, M. Perarnau-Llobet, M. Huber, and A. Acin, Phys. Rev. Lett. 111, 240401 (2013)

    work page 2013

  16. [16]

    Francica, Phys

    G. Francica, Phys. Rev. E 111, 014141 (2025)

    work page 2025

  17. [17]

    Binder, S

    F. Binder, S. Vinjanampathy, K. Modi, and J. Goold, New J. Phys. 17, 075015 (2015)

    work page 2015

  18. [18]

    Campaioli, F

    F. Campaioli, F. A. Pollock, F. C. Binder, L. C ´eleri, J. Goold, S. Vinjanampathy, and K. Modi, Phys. Rev. Lett. 118, 150601 (2017)

    work page 2017

  19. [19]

    J.-Y. Gyhm, D. ˇSafr´anek, and D. Rosa, Phys. Rev. Lett. 128, 140501 (2022)

    work page 2022

  20. [21]

    Ferraro, M

    D. Ferraro, M. Campisi, G. M. Andolina, V. Pellegrini, and M. Polini, Phys. Rev. Lett. 120, 117702 (2018)

    work page 2018

  21. [22]

    G. M. Andolina, M. Keck, A. Mari, M. Campisi, V. Giovannetti, and M. Polini, Phys. Rev. Lett. 122, 047702 (2019)

    work page 2019

  22. [23]

    G. M. Andolina, D. Farina, A. Mari, V. Pellegrini, V. Giovannetti, and M. Polini, Phys. Rev. B 98, 205423 (2018)

    work page 2018

  23. [24]

    Farina, G

    D. Farina, G. M. Andolina, A. Mari, M. Polini, and V. Giovan- netti, Phys. Rev. B 99, 035421 (2019)

    work page 2019

  24. [25]

    Y. Y. Zhang, T. R. Yang, L. Fu, and X. Wang, Phys. Rev. E 99, 052106 (2019)

    work page 2019

  25. [26]

    G. M. Andolina, M. Keck, A. Mari, V. Giovannetti, and M. Polini, Phys. Rev. B 99, 205437 (2019)

    work page 2019

  26. [27]

    Crescente, M

    A. Crescente, M. Carrega, M. Sassetti, D. Ferraro, Phys. Rev. B 102, 245407 (2020)

    work page 2020

  27. [28]

    Rossini, G

    D. Rossini, G. M. Andolina, and M. Polini, Phys. Rev. B 100, 115142 (2019)

    work page 2019

  28. [29]

    Rossini, G

    D. Rossini, G. M. Andolina, D. Rosa, M. Carrega, and M. Polini, Phys. Rev. Lett. 125, 236402 (2020)

    work page 2020

  29. [30]

    D. Rosa, D. Rossini, G. M. Andolina, M. Polini, and M. Carrega, J. High Energ. Phys. 2020, 67 (2020)

    work page 2020

  30. [31]

    Carrega, J

    M. Carrega, J. Kim, and D. Rosa, Entropy 2021, 23(5), 587 (2021)

    work page 2021

  31. [32]

    Gyhm, and U

    J.-Y. Gyhm, and U. R. Fischer, AVS Quantum Sci. 6, 012001 (2024)

    work page 2024

  32. [33]

    Francica, Phys

    G. Francica, Phys. Rev. A 110 6, 062209 (2024). Phys. Rev. A 111, 019901 (2025)

    work page 2024

  33. [34]

    Bhatia, and C

    R. Bhatia, and C. Davis, The American Mathematical Monthly 107 (4): 353-357 (2000)

    work page 2000

  34. [35]

    Jarzynski, Phys

    C. Jarzynski, Phys. Rev. Lett. 78, 2690 (1997)

    work page 1997

  35. [36]

    G. E. Crooks, Phys. Rev. E 60, 2721 (1999)

    work page 1999

  36. [37]

    A Quantum Fluctuation Theorem

    J. Kurchan, arXiv:cond-mat/0007360 (2000)

    work page internal anchor Pith review Pith/arXiv arXiv 2000

  37. [38]

    Jarzynski Relations for Quantum Systems and Some Applications

    H. Tasaki, arXiv:cond-mat/0009244 (2000)

    work page internal anchor Pith review Pith/arXiv arXiv 2000

  38. [39]

    Talkner, E

    P. Talkner, E. Lutz, and P. H ¨anggi, Phys. Rev. E 75, 050102(R) (2007)

    work page 2007

  39. [40]

    Campisi, P

    M. Campisi, P. H ¨anggi, and P. Talkner, Rev. Mod. Phys. 83, 771 (2011)

    work page 2011

  40. [41]

    Perarnau-Llobet, E

    M. Perarnau-Llobet, E. B¨aumer, K. V. Hovhannisyan, M. Huber, and A. Acin, Phys. Rev. Lett. 118, 070601 (2017)

    work page 2017

  41. [42]

    B ¨aumer, M

    E. B ¨aumer, M. Lostaglio, M. Perarnau-Llobet, and R. Sampaio (2018). Fluctuating Work in Coherent Quantum Systems: Pro- posals and Limitations. In: F. Binder, L. Correa, C. Gogolin, J. Anders, and G. Adesso, (eds) Thermodynamics in the Quantum Regime. Fundamental Theories of Physics, vol 195. Springer, Cham

    work page 2018

  42. [43]

    Gherardini, and G

    S. Gherardini, and G. De Chiara, PRX Quantum 5, 030201 (2024)

    work page 2024

  43. [44]

    D. R. M. Arvidsson-Shukur, W. F. Braasch Jr., S. De Bi `evre, J. Dressel, A. N. Jordan, C. Langrenez, M. Lostaglio, J. S. Lundeen, and N. Y. Halpern, New J. Phys. 26, 121201 (2024)

    work page 2024

  44. [45]

    A. E. Allahverdyan, Phys. Rev. E 90, 032137 (2014)

    work page 2014

  45. [46]

    Solinas, and S

    P. Solinas, and S. Gasparinetti, Phys. Rev. E 92, 042150 (2015)

    work page 2015

  46. [47]

    Lostaglio, A

    M. Lostaglio, A. Belenchia, A. Levy, S. Hern ´andez-G´omez, N. Fabbri, and S. Gherardini, Quantum 7, 1128 (2023)

    work page 2023

  47. [48]

    Lostaglio, Phys

    M. Lostaglio, Phys. Rev. Lett. 120, 040602 (2018)

    work page 2018

  48. [49]

    Francica, Phys

    G. Francica, Phys. Rev. E 105, 014101 (2022)

    work page 2022

  49. [50]

    Francica, Phys

    G. Francica, Phys. Rev. E 106, 054129 (2022)

    work page 2022

  50. [51]

    Francica, and L

    G. Francica, and L. Dell’Anna, Phys. Rev. E 109, 044119 (2024)

    work page 2024

  51. [52]

    Francica, and L

    G. Francica, and L. Dell’Anna, Phys. Rev. A 109, 052221 (2024)

    work page 2024

  52. [53]

    Francica, and L

    G. Francica, and L. Dell’Anna, Phys. Rev. E 109, 064138 (2024)

    work page 2024

  53. [54]

    Francica, and L

    G. Francica, and L. Dell’Anna, Phys. Rev. E 108, 014106 (2023)

    work page 2023

  54. [55]

    Julia-Farre, T

    S. Julia-Farre, T. Salamon, A. Riera, M. N. Bera, and M. Lewen- stein, Phys. Rev. Research 2, 023113 (2020)

    work page 2020

  55. [56]

    A. J. Leggett, and A. Garg, Phys. Rev. Lett. 54, 857 (1985)

    work page 1985

  56. [57]

    H. J. D. Miller, J. Anders, Entropy 20, 200 (2018)

    work page 2018